Accomodations

Hello,
I’m going to Europe for the first time in October with my girlfriend and I’m having a hard time finding a hostel or hotel with a fair price. Is there no place to stay in london for a reasonable price?
I prefer to stay in a private room. In other countries that I have searched it’s cheaper to stay in a hotel than in a private room in a hostel.
I’ve been looking in booking.com and using eurotrip’s search engine, but I couldn’t find anything vlose to 50-60 pounds a day, except for the “easyhotel.com”. Is it good?